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Basics of Astronomy28 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Artem Cheprasov*

Find out about the interesting life and major contributions of Johannes Kepler. This lesson will also teach you how to find out how long it takes a planet to revolve around the sun!

**Johannes Kepler** was a German astronomer and mathematician born in 1571 to a poor family. His story is one of overcoming some serious difficulties to become one of the greatest astronomers of all time. His father was an interesting figure. He was a mercenary that fought for the highest bidder and eventually failed to come home after an expedition. I wonder what happened? His mother was no less interesting as she was accused of witchcraft, and Kepler had to defend her in a trial.

In spite of all of this and poor health, Kepler was a good student and got a scholarship to go to a university in order to become a Lutheran pastor. As he was finishing his studies, he got a job teaching math and astronomy. Ironically, he did not like these jobs, claiming he knew very little of either. Perhaps owing to this, he had few students his first year and none at all his second year! Talk about bad professor reviews!

Anyways, while still in college, Kepler learned as much as possible about astronomy and believed in the Copernican hypothesis, the one that had the sun at the center of the then-known universe.

He eventually published a book, where many of his thoughts on astronomy were way off by modern standards. However, the book did show to the world that he was a talented mathematician.

Kepler sent a copy of his book to none other than Galileo and Tycho Brahe, a Danish astronomer. Tycho was probably the most famous astronomer of his day. So when Tycho invited Kepler to become his assistant in Prague in 1600, you better believe Kepler readily accepted. The next year, Tycho died, and Kepler became an imperial mathematician.

Thanks to Tycho's meticulous observations of planetary motion, Kepler began to study and observe the motion of Mars and, using his exceptional math skills, had figured out the true orbital nature of Mars by 1606. He found out that it actually moved in a very slightly elongated ellipse. Such a discovery completely quashed 2000 years of belief that the planets moved in a circle.

Kepler also discovered that the planets do not move at the same speed throughout the ellipse. Instead, they move faster when they are closer to the sun. His results were published in a book called *Astronomia Nova (New Astronomy)*.

Before we get to Kepler's laws of planetary motion, which I sort of already gave away, I want to define what an **ellipse** actually is so you can understand one of Kepler's laws a bit better.

An ellipse is a curve surrounding two points, called foci, so that the total distance from one focus to a point on the ellipse and back to the other focus is constant for every point on the curve.

Knowing this, it'll be easier to understand the definition of **Kepler's first law**, which says that the orbit of a planet around the sun is an ellipse, with the sun at one focus. Well, technically, ellipses, the orbits, are nearly circular, and this just reinforces that notion of how amazing Kepler's math was and how precise Tycho's observations were.

**Kepler's second law** states that a line drawn from a planet to the sun always sweeps over equal areas in equal intervals of time. This is just as easy to understand as the first law despite sounding quite difficult. Take a look at the diagram on the screen.

**Kepler's third law** states that the square of the orbital period of a planet is proportional to the cube of its semi-major axis.

The **orbital period** is the time it takes a planet to travel around the sun one time.

The semi-major axis is equal to the planet's average distance from the sun.

Take a look at the equation representing Kepler's third law on the screen. The 'P' stands for the orbital period in 'y' years. The little 'a' stands for the semi-major axis of a planet's orbit, which is measured in AU, or astronomical units.

Knowing all of this, we can use this equation in an example. Jupiter's average distance from the sun is about 5.2 astronomical units. When you cube this number, you get an answer of roughly 140. Therefore, you need to take the square root of both sides to get its orbital period. The square root of 140 is just under 12 years, and this is Jupiter's orbital period!

Math is no fun for most people, so we'll stop the lesson right there!

**Johannes Kepler** was a German astronomer and mathematician who thought he wasn't very good at math or astronomy, only to become a revolutionary astronomer and brilliant mathematician.

Using keen observations compiled by astronomer Tycho Brahe and his own exceptional mathematical skills, Kepler came up with three laws of planetary motion.

**Kepler's first law** says that the orbit of a planet around the sun is an ellipse, with the sun at one focus. An **ellipse** is a curve surrounding two points, called foci, so that the total distance from one focus to a point on the ellipse and back to the other focus is constant for every point on the curve.

**Kepler's second law** states that a line drawn from a planet to the sun always sweeps over equal areas in equal intervals of time.

**Kepler's third law** says that the square of the orbital period of a planet is proportional to the cube of its semi-major axis.

The **orbital period** is the time it takes a planet to travel around the sun one time, and the semi-major axis is equal to the planet's average distance from the sun.

Study this lesson as you aim for these objectives:

- Display knowledge of the life and achievements of Johannes Kepler
- Discuss Kepler's partnership with Tycho Brahe
- Outline and explain Kepler's first, second and third laws of planetary motion
- Recall the equation for Kepler's third law

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Basics of Astronomy28 chapters | 325 lessons

- Go to Telescopes

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- Geocentric, Heliocentric & Ptolemaic Models of the Universe 6:23
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